We are given a sequence ${a_n}$ such that $a_1 = 1$ and $a_{n+1} = 3a_n + 2$. We need to find the value of $a_4$.

1. Problem Description

We are given a sequence ${a_n}$ such that $a_1 = 1$ and $a_{n+1} = 3a_n + 2$. We need to find the value of $a_4$.

2. Solution Steps

We are given the recursive formula $a_{n+1} = 3a_n + 2$ and $a_1 = 1$.

We can use this to find $a_2, a_3, a_4$.

$a_2 = 3a_1 + 2 = 3(1) + 2 = 5$

$a_3 = 3a_2 + 2 = 3(5) + 2 = 15 + 2 = 17$

$a_4 = 3a_3 + 2 = 3(17) + 2 = 51 + 2 = 53$

3. Final Answer

$a_4 = 53$